The exercises in this section prepare the reader for the next three chapters instead of dealing with the PDEs. An interested reader will find several useful problems in Betounes (1998).

Let X_t be a geometric Wiener process,

X_t = e^Y,

Where

Yt ? N(?t, ?²t).

(a) Consider the definition

And the trivaial equality

Using these, calculate the expectation:

E[X,JX, s < ]= E[eY,s < 1). Y-Y,.s < t). E[e" |Y, s < 1]- E[-Y,H Y,s < 1]. E[X, X,, s < 1].